1. Field of the Invention
The present invention relates to a signal processing method of generating four signals representing intensities of four different colors to represent a color of one pixel from three signals designating a color of one pixel by mixing colors, an image display apparatus, and a Television apparatus.
2. Description of the Related Art
Conventionally, a display such as a TV set or a computer display monitor has displayed an image by using a light's three primary colors. In other words, various colors can be represented in such a manner that a pixel is composed of each sub pixel of Red (R), Green (G), and Blue (B) and the intensities of the lights of R, G, and B are changed using principles of a parasynthetic mixed color and an additive mixed color. The colors capable of being reproduced by this display is within a range that can be represented by a sum represented by a vector of three primary colors, R, G, and B.
FIG. 9 illustrates a color range, which can be reproduced by a display of three primary colors, by a three-dimensional vector. In an example shown in FIG. 9, as a coordinate space showing a position of R, G, and B on a three dimension, a CIE 1931 color coordinate system (an X, Y, and Z color coordinate system) is used. Then, a coordinate when R takes the highest value is defined as (XR, YR, ZR), a coordinate when G takes the highest value is defined as defined as (XG, YG, ZG), and a coordinate when B takes the highest value is defined as (XB, YB, ZB). In this case, the display can indicate the inside color of a hexahedron shown in FIG. 9.
In addition, only from the perspective of a chromaticity, a color reproduction range can be also represented by using an x and y chromaticity coordinate (an xy chromaticity diagram) of an X, Y, and Z color coordinate system. In this case, the color reproduction range is an area encircled by a triangle of FIG. 10.
In the display of three primitive colors, a color D having a coordinate of (XD, YD, and ZD) can be shown as “a mathematical expression 1” assuming that coefficients of the three primitive colors, R, G, and B are r, g, and b (the values of 0 to 1 are within an effective range, respectively).{right arrow over (D)}r×{right arrow over (R)}+g×{right arrow over (G)}+b×{right arrow over (B)}  <Mathematical Expression 1>
Where D, R, G, and B are vectors from original points (0, 0, and 0) into D, R, G, and B, respectively.
Transforming “Mathematical Expression 1” and representing it by a matrix calculation, “Mathematical Expression 2” is formed.
                                          (                                                                                X                    D                                                                                                                    Y                    D                                                                                                                    Z                    D                                                                        )                    =                                    M              3                        ·                          (                                                                    r                                                                                        g                                                                                        b                                                              )                                      ,                                  ⁢                              M            3                    =                      (                                                                                X                    R                                                                                        X                    G                                                                                        X                    B                                                                                                                    Y                    R                                                                                        Y                    G                                                                                        Y                    B                                                                                                                    Z                    R                                                                                        Z                    G                                                                                        Z                    B                                                                        )                                              <                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          2                >            
Accordingly, the coefficients r, g, and b for representing the color D are obtained as shown in “Mathematical Expression 3”.
                              (                                                    r                                                                    g                                                                    b                                              )                =                              M            3                          -              1                                ·                      (                                                                                X                    D                                                                                                                    Y                    D                                                                                                                    Z                    D                                                                        )                                              <                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          3                >            
In recent years, there has been an attempt to use four or more primary colors so as to broad the color reproduction range for this display of three primary colors. Thereby, a color that could not be represented by a conventional display can be reproduced and it is possible to improve color reproducibility and obtain a high realistic sensation.
In a display of n (n is an integer number of 3 or more) primary colors, the X, Y, and Z coordinate of (XD, YD, and ZD) of the display colors for the value of each primary color is obtained as shown in “Mathematical Expression 4”.
                                          (                                                                                X                    D                                                                                                                    Y                    D                                                                                                                    Z                    D                                                                        )                    =                                    M              n                        ·                          (                                                                                          c                      ⁢                                                                                          ⁢                      1                                                                                                                                  c                      ⁢                                                                                          ⁢                      2                                                                                                                                  c                      ⁢                                                                                          ⁢                      3                                                                                                            ⋮                                                                                        cn                                                              )                                      ,                                  ⁢                              M            n                    =                      (                                                                                X                                          c                      ⁢                                                                                          ⁢                      1                                                                                                            X                                          c                      ⁢                                                                                          ⁢                      2                                                                                                            X                                          c                      ⁢                                                                                          ⁢                      3                                                                                        ⋯                                                                      X                    cn                                                                                                                    Y                                          c                      ⁢                                                                                          ⁢                      1                                                                                                            Y                                          c                      ⁢                                                                                          ⁢                      2                                                                                                            Y                                          c                      ⁢                                                                                          ⁢                      3                                                                                        ⋯                                                                      Y                    cn                                                                                                                    Z                                          c                      ⁢                                                                                          ⁢                      1                                                                                                            Z                                          c                      ⁢                                                                                          ⁢                      2                                                                                                            Z                                          c                      ⁢                                                                                          ⁢                      3                                                                                        ⋯                                                                      Z                    cn                                                                        )                                              <                  Mathematical          ⁢                                          ⁢          Expression          ⁢                                          ⁢          4                >            
Where c1, c2, c3, . . . , and cn are coefficients of respective primary colors, and (Xc1, Yc1, Zc1), (Xc2, Yc2, Zc2), . . . (Xcn, Ycn, Zcn) are X, Y, and Z coordinates of respective primary colors. In order to obtain a coefficient of each primary color from the X, Y, and Z values to be displayed, an inverse matrix of a matrix Mn should be calculated as shown in “Mathematical Expression 3”. However, the matrix Mn is a matrix of 3×n, so that the inverse matrix thereof cannot be directly obtained.
Japanese Patent Application Laid-Open (JP-A.) No. 6-261332 discloses a method of displaying a color of a range, which could not be displayed by a conventional TV set of RGB three primary colors, by using six primary colors. According to a first example of JP-A. No. 6-261332, the transmitted image signal is converted into an RGB signal, and then, it is converted into an XY chromaticity coordinate so as to obtain the position where the XY chromaticity coordinate is located on the xy chromaticity diagram. When displaying colors, four combinations of three primary colors, which are not overlapped each other, are selected from among six primary colors in advance. This is shown by a chromaticity diagram as FIG. 11, and determining to which of four triangles the color to be displayed belongs, this color is displayed using three primary colors making an apex of the triangle, to which this color belongs.
In addition, as disclosed in JP-A. No. 2000-338950, there is a system of converting the inputted tristimulus value into a color image signal by providing means of determining in which area the color to be displayed is located in a three-dimensional color space capable of being displayed by four primary colors. In the case of four primary colors, a color within a three-dimensional figure as shown in FIG. 10A can be reproduced. In JP-A. No. 2000-338950, determining in which three-dimensional figure in FIGS. 10B to 10E the color to be displayed is included, the value of each primary color is obtained due to the same calculation as “Mathematical Expression 2” using the coordinate of the apex of the hexahedron encircling that color. This determination is carried out by calculating the coefficient of each primary color in FIGS. 12B to 12E using “Mathematical Expression 2” and checking whether all coefficients are covers by a range of 0 to 1 or not.
In JP-A. No. 2004-152737, as a method of converting the tristimulus value into a color image signal, a method of obtaining an inverse conversion of a 3×4 matrix by using a pseudo inverse matrix is exemplified.
In addition, in “collected papers of color forum JAPAN '97 (1997, PP. 13 to 16), a method is described, in which a ratio of coefficients of respective primary colors is calculated so that they have the highest luminance, which can be indicated by a display in the same xy chromaticity coordinate as that of the color to be displayed, to multiplex each coefficient with the value so as to obtain a desired luminance.